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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 4002.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4002.j1 | 4002i1 | \([1, 1, 1, 1735, 245063]\) | \(577572497126639/26125579653696\) | \(-26125579653696\) | \([]\) | \(10080\) | \(1.2543\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 4002.j1 has rank \(1\).
Complex multiplication
The elliptic curves in class 4002.j do not have complex multiplication.Modular form 4002.2.a.j
sage: E.q_eigenform(10)